1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ICE Princess25 [194]
2 years ago
12

Find the derivative of the following function, with a positive index (differentiation)

Mathematics
1 answer:
Yakvenalex [24]2 years ago
6 0

Answer:

2nd option

Step-by-step explanation:

Using the power rule

\frac{d}{dx} (ax^{n} ) = nax^{n-1}

Given

f(x) = \frac{3}{2\sqrt[3]{x} } = \frac{3}{2x^{\frac{1}{3} } } = \frac{3}{2} x^{-\frac{1}{3} } , then

f'(x) = - \frac{1}{3} × \frac{3}{2} x^{-\frac{4}{3} }

      = - \frac{1}{2} × \frac{1}{x^{\frac{4}{3} } }

      = - \frac{1}{2x^{\frac{4}{3} } } = - \frac{1}{2\sqrt[3]{x^4} } [ Note there should be a leading negative ]

You might be interested in
A motor vehicle has a maximum efficiency of 39 mpg at a cruising speed of 40 mph. The efficiency drops at a rate of 0.1 mpg/mph
svp [43]

Answer:

38 mpg

Step-by-step explanation:

Initial efficiency = 39 mpg

Initial speed = 40 mph

Final speed = 50 mph

The efficiency drop  between 40 mph and 50 mph is given by:

E_d = 0.1 \frac{mpg}{mph}*\Delta V

The total efficiency drop from 40 to 50 mph is:

E_d = 0.1 \frac{mpg}{mph}*(50-40)mph\\E_d = 1\ mpg

Therefore, the efficiency at 50 mph is:

E_{50} = E_{40} -E_d\\E_{50} = 39 -1\\E_{50} = 38\ mpg

5 0
3 years ago
Need answer asap, will give brainliest.
Nesterboy [21]

The solution is the point where the lines cross. So (-1, -2)

6 0
2 years ago
Need help with geometry problem
Aloiza [94]
This one is similar to the previous one.

6 0
2 years ago
There are 18 students on the math team of these 5 are boys give the ratio of boys to girls on the math team in simplest form
Viefleur [7K]

Answer:

The answer is 5/13 or 5:13

Step-by-step explanation:

There are 18 students in total. And among them there are 5 boys. You would do

18-5=13

5 boys

13 girls

Mark Brainliest Please :)

7 0
2 years ago
Read 2 more answers
What is the vertex of g(x) = 8x2 - 48x + 65?<br> O (-3,-7)<br> O (3.-7)<br> O (24,-7)<br> O (-24,-7)
yanalaym [24]

Answer:

The answer is B (3.-7)

Step-by-step explanation:

If you graph it the vertex is the top of the curve

6 0
3 years ago
Read 2 more answers
Other questions:
  • 25% of what number equals 7?
    7·2 answers
  • What simple machine is similar to a pulley?
    14·1 answer
  • Charles wants to find out if the students in foreign language classes spend more time in class speaking in English or in the for
    14·2 answers
  • Find the distance between the point (3,-1) and (-2,3)?
    8·1 answer
  • Can anyone tel me what y equals in standard form?
    7·2 answers
  • Clas problem set for basic cross multiplying
    7·1 answer
  • The dot plot shows the number of classes per semester that a group of boys and girls have chosen to take in their freshman year
    7·2 answers
  • Find a in 211afour= 150
    15·1 answer
  • An angle measures 2° more than the measure of its supplementary angle. What is the measure of each angle?
    5·1 answer
  • 2/3x=4 <br><br> Group of answer choices<br><br> a. x= 8<br><br> b. x= 6<br><br> c. x = 8/3
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!